The Cauchy Integral Theorem is a fundamental result in complex analysis, stating that if a function is holomorphic (complex differentiable) within a simply connected domain, then the integral of that function over any closed curve in that domain is zero. This means that the value of the integral does not depend on the path taken, as long as the path remains within the domain. This theorem is crucial for understanding the behavior of complex functions and leads to other important results, such as the Cauchy Integral Formula. It highlights the significance of analytic functions and their properties in the field of mathematics.